He arrives at Anfield after British media reported Liverpool paid a 70 million euros release clause in his contract.
Szoboszlai becomes the club's second recruit under new sporting director Jorg Schmadtke after Argentine Alexis Mac Allister (24) as Liverpool look to revamp their midfield following a disappointing season.
"The last three or four days went really long, it was not that easy. But at the end I'm here, I'm happy and I can't wait to get started," Szoboszlai said in a statement.
"(A) really historic club, really good players, good coach, everything is good. For me it was perfect to make the next step in a club like this. The fans, the stadium, everything is really good."
The Hungary international scored 20 goals and provided 22 assists in 91 games since joining Leipzig in the 2021 winter transfer window.
Szoboszlai helped Leipzig win back-to-back German cups, and scored their second goal as the beat Eintracht Frankfurt 2-0 in last season's final in early June.
A set-piece specialist with an eye for goal and the ability to play across the midfield, Szoboszlai will wear the number eight shirt once worn by Liverpool great Steven Gerrard and recently vacated by Naby Keita.
Liverpool manager Juergen Klopp said he had seen Szoboszlai first hand when the midfielder was a teenager at Red Bull Salzburg, adding that he had made great strides since in the Bundesliga while also captaining Hungary at a young age.
"These are proper positives and this is even before we even think about his qualities as a footballer," Klopp said.
"I will not say too much about them at this stage except they are definitely the kind which will hopefully bring a lot of enjoyment and also help us to get results.
"There is no pressure, though. Dominik is still a very young player. He has so much development ahead of him and this means it makes sense for us all to be patient and to give him the time and space to allow his talent to come through within our team."
Szoboszlai is the second key player to leave Leipzig for the Premier League in the close season after Chelsea snapped up French forward Christopher Nkunku (25) on a six-year deal.